# What is the formula for two (or more) tone amplitude modulated signal?

by tfr000
Tags: amplitude, formula, modulated, signal, tone
 P: 119 So far I have: V=Acarriersin(2∏Fcarriert) (1+Cmodsin(2∏F1t)+Cmodsin(2∏F2t)) which I think is pretty close to correct. Where: A is amplitude, F is freq, t is time, Cmodis the coefficient of modulation, i.e. 1=100% modulation. I can find plenty of websites offering 1-tone AM, but not 2 or more tones. You actually have to mess with Cmod, because if you use 1, you get 200% modulation with two tones... I think.
P: 2,751
 Quote by tfr000 So far I have: V=Acarriersin(2∏Fcarriert) (1+Cmodsin(2∏F1t)+Cmodsin(2∏F2t)) which I think is pretty close to correct. Where: A is amplitude, F is freq, t is time, Cmodis the coefficient of modulation, i.e. 1=100% modulation. I can find plenty of websites offering 1-tone AM, but not 2 or more tones. You actually have to mess with Cmod, because if you use 1, you get 200% modulation with two tones... I think.
It's perhaps easier to consider it terms of a general modulating (message) signal $x_m(t)$.

If we normalize the modulating signal such that $-1 \le x_m(t) \le 1$ then the AM signal can be written as:

$$v = A \sin(w_c t) (1 + M \, x_m(t))$$

Where A is the carrier amplitude and M is the modulation index.
P: 119
 Quote by uart It's perhaps easier to consider it terms of a general modulating (message) signal $x_m(t)$. If we normalize the modulating signal such that $-1 \le x_m(t) \le 1$ then the AM signal can be written as: $$v = A \sin(w_c t) (1 + M \, x_m(t))$$ Where A is the carrier amplitude and M is the modulation index.
OK, that makes sense. My equation reduces to yours with xm = (sin(2∏F1t) + sin(2∏F2t)) and M = Cmod... and a bunch of sleight of hand regarding ω and 2∏f. Thanks!

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